Monday, November 29, 2010

I'm Making Toast

My last post claimed that the relationship between the settings on a toaster and the time spent toasting is not a linear relationship.  I worked this out using Dan Meyer's data from his blog dy/dan.  Dan responded that one data point changed the distribution.  I'm pretty sure that he is right, but judging from this comment by Dan, neither of us will rest until this is settled.

I've decided to collect my own data.  I'm recording the air temperature inside of the toaster to make sure that I start each trial at 80 degrees Fahrenheit.  I'm also setting the toaster randomly.  I have a super-geeky way to do make the random selections, as you can see below.

This is a slow process, as it takes 10 to 15 minutes for the  toaster to cool.  Hopefully I can finish collecting my data before the sacrificial loaf goes stale.  I'll have to write another NSF grant if it does.

Friday, November 26, 2010

Toasting Time is Not Linear

Dan Meyer just posted some data on his dy/dan blog about toaster settings vs. toasting time.  You can see the video posted below.

Meyer — Toaster Regression from Dan Meyer on Vimeo.

I just ran the toasting times through Microsoft Excel 2010.  The raw data is below.
Raw Data

I graphed the data and used trendlines to analyze the data.  The first graph shows the linear regression.
Linear Regression

The next graph is the exponential regression.
Exponential Regression

Finally, here is the quadratic regression.
Quadratic Regression
Based on the correlation values, the best model is the quadratic.  The exponential is second best.  The linear is the third best.  However, all are good representations.

Also on Dan's blog post, the darkness of the toast is estimated.  The graph, with exponential regression, is below.

Wednesday, November 24, 2010

So, I Used WolframAlpha in Class After All

I gave an example in College Algebra yesterday about the U.S. GDP and Chinese GDP.  We were talking about exponential functions, and I made up some numbers and asked the students to find when the Chinese GDP would be larger than the U.S. GDP.  The year we got with my numbers was 2049.  After I finished the example, I told the students about Hans Rosling's talk on TED about when Asian per capita income would be larger then the U.S. per capita income.  He came up with the year 2048.

I was amazed how close our dates were, even though he is using real data and I just made up numbers.  So, I showed the class WolframAlpha and we were able to find graphs of the Chinese GDP and U.S. GDP over the past sixty years.   Both graphs generated by WolframAlpha looked appropriately exponential.

I was wrong about the starting values for the economies in 2000 (I guessed 4 trillion dollars for the US and 400 billion dollars for China) but the ratio between my guesses and the actual values was correct (10 trillion for the US and 1 trillion for China).  I was confident in my estimates for the growth rate for both economies (4% for the U.S. and 9% for China) because I got them off of the news over the past few years.

In my last post, I discussed overuse of programs like WolframAlpha in teaching.  I felt like a hypocrite when I used WolframAlpha in class.  In my defense, I never did say it was a bad program, just that it shouldn't be the foundation for a mathematics curriculum.  For the record, we did solve the equation that we developed in class by using graphing calculators.

Friday, November 19, 2010

Whose Computer Can Solve This for Me?

There's an scene in The Simpsons where Edna Krabappel is teaching the students math.  The dialogue is below.
Mrs. Krabappel: Now, whose calculator can tell me what 7 times 8 is?
Milhouse: Oh! Oh! Oh! Low Battery?
Mrs. Krabappel: Whatever.
 I was reminded of this scene when I saw this talk by Conrad Wolfram on the TED website.

I found a link to the talk on this post by Maria Andersen.

The modern version of The Simpsons scene would have Bart's class in a computer lab.  The dialogue would be the following.

Mrs. Krabappel: Whose computer can compute this integral for me?
Milhouse: Oh! Oh! Oh! 404
Mrs. Krabappel: What's the whole answer?
Milhouse: 404 Error: Page not Found
The thesis of the Wolfram's talk is that the mathematics taught in school today does not reflect the real world.  Also, requiring calculations to be done by hand is the bottleneck preventing students working on real world problems.  His solution is to use a program like WolframAlpha, which can solve many mathematics problems automatically, with students.

I do agree with his statement of the problem.  I do have a few points of disagreement with his solution.
  1. Graphing calculator do quite well with teaching mathematics.  At my college, we use graphing calculators at all levels of algebra.  Our College Algebra class is modeling based, so we make heavy use of calculators.  We teach graphing operations, statistical operations, and using the solver application.

    Access to calculators is not a limitation.  The local high schools require the TI-84 calculator, and most of our students still have theirs.  Also, the college has some available for students to borrow.

    The calculators do have limitations, but those are not disadvantages.  The calculator can only process the mathematics that the students put into the calculator.  That means that the students have to develop or find the formula to measure how drunk is someone on their own.  Also, the computers are too fast in presenting the results.  Calculators require the students to slow down and see the fine details.  Finally, calculators cannot get information off of the internet.  Any communication device is also a cheating device.
  2. There is no silver bullet to fix mathematics education.  The problem is that there is a new silver bullet every five years or so.  At some point, people outside of the teaching profession are going to have to realize that people learn in unique ways.  Wolfram is not alone in thinking that he has found the solution.  Some colleges are changing all developmental (below college level) mathematics courses to computer delivered instruction.  This mode of learning only engages two senses.  Three if you count the soreness in your butt from all the sitting.
  3. Computers do not let students feel mathematics instinctively.  Our instincts are not wired for computer simulations or moving sliders with a mouse.  Our instincts are wired for dealing with the tactile world.  To teach surface area, let the students count the tiles on the floor.  Let them see what a square foot looks like.  To teach linear functions, let the students walk down the hallway and make distance and time measurements.  To teach surface area, let the students paint a box and see how much paint they use.
  4. Don't use programming to teach elementary mathematics.  This is adding a layer of difficulty and abstraction on top of a difficult subject.  I know that I would learn well using this technique, but I also know I am rare in this learning style.
  5. It is not true that all calculations have been done by hand except in the last few decades.  My abacus and slide rule want to know what you meant by this, Conrad.
I don't disagree with Wolfram that there is a problem with how mathematics has been taught in the past.  I am concerned by anybody who claims there is a single solution to the problem.  Computers have a part in the mathematics curriculum, but they must not upstage the rest of the valid learning techniques.

Wednesday, November 17, 2010

I'm Done with Twitter

I couldn't find a use for Twitter.  I also haven't had anything to tweet for three days.  If I ever figure out a use for Twitter, I'll post it on the blog.

Sunday, November 14, 2010

Can We Know the Sources of Pseudocontext?

There is a saying that a camel is a horse designed by committee.  I am starting to think that textbooks suffer from the same problem.

On the blog dy/dan, there is a comment by josh g. on pseudocontext.  He is responding to my comment. Here is an excerpt of josh's comment.
I guess that’s part of why I keep coming back to trying to imagine the process in which these kinds of problems get written. We should be able to critique these problems in a way that deconstructs where these things come from, not one that just points the fingers at particular authors or even just specific problems.
I agree with josh completely.  I think that those of us who are worried about pseudocontext are starting to be able to see the boundary between context and pseudocontext.  So, looking for specific examples is not as important now.

What I did learn about textbook writing this week is that there are many different people who are involved in the process.  There is the author, project manager (I met two at the dinner), the editor, the supplemental materials authors, and the reviewers.  I guess that a textbook is the camel designed by committee.

I asked several different people about who controls the content of the text book.  Everybody answered that the authors have a lot of freedom in the content of the text.  Every problem is written by the authors.  However, one person mentioned that the reviews influence the number and type of exercises in each section.  There are nineteen reviewers for the textbook from which I took the example from the post.  I've seen texts with a full page of reviewers' names.

So, imagine that you are a textbook author and you just finished your masterpiece of a text.  The reviews come in, and the editor says that you need to include three more word problem in the section on systems of linear equation, and fifty new word problems in the entire text.  You have to get everything done next week so that the publisher can get the book to print, incorporate your problems into their flagship online homework system, and add them to the solutions manual.  You need to do this on top of your teaching load.

I don't know first hand about publishing a textbook.  If my scenario is far fetched, then please correct me (politely) in the comments.  However, I can see how well intentioned and intelligent authors get stuck with problems that they don't like in their texts.

There are two ways that I can think of to get involved in improving the quality of our textbooks.  Both options require a time commitment on your part.
  1. Become an author.  Textbook companies are looking for authors.  If you have the next great textbook in your head, get it on paper.  You can also self-publish, but be sure to cover all your bases before going that route.
  2. Review textbooks for publishers.  I've been asked once to review textbooks, and that's after only four years of teaching.  I declined because I had six preps that semester.  You could go looking for opportunities.  There is a small amount of money to be earned

AMATYC Boston Day 3

It was my third and final day in Boston.  The conference runs until tomorrow morning, but we usually have to leave early.

Awards Breakfast

The awards breakfast was the only event that I attended today.  The winners of the Student Math League were announced.  Los Angeles City College won the team competition this year.  Congratulations to them.

The keynote address was Infinity Bottles of Beer on the Wall by Lew Lefton.  He told mathematical jokes for forty minutes or so.  I was laughing too hard to keep track of time.  I had heard some of the jokes before.  I wrote one down because it relates to the pseudocontext that we've been talking about.
If you put six white balls and nine black balls in a bag and draw five of them out, then there is a 85% chance you are in a word problem.
After the awards breakfast, I went souvenir shopping and checked out of the hotel.


I'm home now, and my head is swimming.  I've absorbed a lot of information, and I need to distill it.  My ears are still plugged from the flight. 

Friday, November 12, 2010

AMATYC Boston Day 2

It's been a good day today in Boston.  I had a good talk with Gary Rockswold and Terry Krieger and a productive committee meeting with the ITLC.

Sessions for the Day
I started the day with the Innovative Teaching and Learning Techniques Themed Session.  I sat in the following fifteen minute talks.
  1. Promote Active Learning Using Real-World Applications - Frank C. Wilson
    This talk is along the same interests of mine.  The activity was about the dice game Pig and computing associated probabilities.  I think this is a good project, but I don't know if I would consider it "real world".
  2. Digital Learning Projects - Maria Andersen
    There was a lot of information to process.  She had good ideas about students using social media to reflect on and share about their learning.  She also had a good idea about using data visualization.  I am going to look into doing these projects in college algebra and calculus.
  3. Symbolic Processors: Wave of the Future? - Fred Felton
    This talk was about using Wolfram Alpha in the classroom.  I learned later that I misinterpreted Fred's use of this program in his classes.  I am worried about this program because it does all of the work for a student in solving a problem.  I don't want student to believe that technology can replace thinking, and Wolfram Alpha is close to being able to make the replacement.  In addition, I really, really don't like Stephen Wolfram's views on science and mathematics.  I tried to read A New Kind of Science, but could only get through 21 of the 1300 pages before getting too angry to read.
  4. Beyond Tables - Introductory Statistics - Dianna Cichocki
    This was a good talk about using JAVA applets to replace tables of probabilities for normal distributions.  She asked during the talk if we still use tables of trigonometric values in class.  I raised my hand because I still show how to use them in my trigonometry class.  I want students to be aware that there are ways of doing things that don't involve batteries and plugs.  I would never require students to use trig tables instead of calculators.  Dianna is making effective use of the applets in her classroom.
Lunch With Gary Rockswold and Terry Krieger
Pearson, the textbook publisher, arranged a lunch with a few instructors with the authors Gary Rockswold and Terry Krieger.  I thank them for the lunch.
I was fascinated to get the views of the authors and the publisher reps.  We have been discussing pseudocontext on my blog and at dy/dan.  I tried to bring it up with the authors, but I couldn't make myself clearly understood.  I didn't press because I didn't want to be a jerk.

Both the authors, and Gary's daughter Jessica are nice people.  I feel bad for using one of their examples on the dy/dan blog.
Dana's Talk
I went to the talk of one of my coworkers.  It was on grant writing.  I went to show support for Dana.  I don't have much interest in the topic right now.
ITLC Meeting
The Innovative Teaching and Learning Committee had its meeting in the afternoon.  It was a good meeting.  Most of the committee is in favor of proctored exams for online classes.  I was under the impression that the opposite was true.  Proctored tests are very important to me.  The committee is looking into a position paper on online educational resources (OER), with which I have volunteered to help.

I'm much more alert tonight than I was last night.  I am planning on going for a walk around the hotel and the nearby shops to burn off some energy and calories before bed.  I went through Barnes & Noble too quickly last night.

Thursday, November 11, 2010

I Caved on Twitter

I just posted that I was almost convinced to try Twitter.  In a moment of weakness, I signed up.  It was quick and painless.  I promise to never Tweet what I have for breakfast.

AMATYC Boston Day 1

I've had a busy day in Boston today.  It's the first day of the AMATYC Conference.  This is my third year attending the conference.  I'm starting to recognize people from one year to the next.

Morning Sessions

Here is a summary of the sessions I attended.
  1. Collaboration is the Key! - Vicki Gearhart and Honey Kirk
    I thought this was going to be a talk about student collaboration.  I was wrong, but I'm glad I went to the talk anyway.  It was about curriculum alignment in Texas.  The collaboration is between the high schools, community colleges, and four-year colleges.  The point is that the alignment is supposed to be a bottom-up approach, which I like.  Kentucky is going through a similar thing right now, but they are taking a top-down approach.
  2. On the Use of Social Media - Mike Martin, Maria Anderson, Fred Feldon, and Mary Beth Orrange
    You can tell I have an interest in social media because you are reading my blog.  You also can tell that a talk is good if it almost convinces me to sign up for Twitter.  I did say almost. 

    The biggest thing I took away from this talk is that employers are looking to social media in the hiring process.  It would be a good idea to encourage students to leverage their on-line presence to reflect their strengths.

    Maria Andersen showed us Imagination Cubed, a website for sharing drawing.  It can be used for displaying writing on a tablet PC to online students.  It caused a buzz of excitement in the audience.
  3. The Power of Google Docs for Effective Online Course Management - George M. Alexander and Calvin Williamson
    I was hoping to learn more about the mechanics of Google Documents.  I've been using Google Documents as a file server for this blog.  They had good ideas on how to use Google Documents to replace a course management system like Blackboard.  It looks like a good alternative.

    The problem I have with intirely online classes is that you can never know who is really doing the work.  If there is one class that would make an otherwise honest student cheat, it's math.
  4. I Can't Teach Calculus and It's Not My Fault! - Philip Cheifetz
    This talk did a good job highlighting the difficulty with falling standards.  The main point was that students are passing Precalculus and Calculus I with such weak skills that they can't do the work for Calculus II.  Dr. Cheifetez made a good case for mastery learning.
  5. Second Life in Higher Education - Fred Felton
    Fred Felton really enjoys Second Life.  I don't see the point.  I think that Second Life is one delivery method for distance learning courses, but not the best.  My concern with Second Life is that it can be so addicting for some people that it would negate any educational benefit.  I joked in the talk that I wish I could make MyMathLab so addicting.

    During the talk, Fred talked about Booland, where you can do virtual bungee jumping and hang gliding.  It seems a little odd to me that you would want to do those things virtually.  I thought the whole point was the adrenaline rush from risking your life.  How would you get that from your basement?
Opening General Session

The Opening General Session had the presentation of the Mathematics Excellence Award.  The two winners were Sadie Bragg and Ed Laughbaum.  Both winners have impressive experience in teaching mathematics and are worthy winners.  The keynote address was The Treasure of Polynomials  by Javier Gomez-Calderon.

AMATYC Exhibits

There are many companies that make their money off of students, and they are all selling their wares here.  The exhibits are popular because of the freebies.  I did grab a few things for the kids, but I don't go Christmas shopping.  The exhibits that I especially noticed were
  1. The MAA - They were giving out pi temporary tattoos.  I grabbed two for the kids.
  2. Easy Worksheet - They have worksheets for free download.  I'll be checking it out soon.
  3. AMSER - The Applied Math and Science Education Repository.  They have free materials for teachers.  Free is my favorite word.
  4. Minitab - I grabbed a t-shirt from them.  I didn't pack enough.
  5. Pearson Publishing - I grabbed a couple of foam puzzles for the kids.
After visiting the exhibition hall, I was wiped out.  I left my coworkers and headed out for dinner by myself.  I got pizza at the food court at the mall across the street.  I bought an abacus at Barnes and Noble,and two pairs of socks.  Now, I am watching Big Bang Theory.  I love it when Wil Wheaton is on.

It's going to be an early night for me.  I'll be meeting my coworkers for breakfast at 7:30 for breakfast in the lobby.

Monday, November 8, 2010

AMATYC Student Math League - Round 1

Maysville Community and Technical College participated in the Student Math League organized by AMATYC.  This semester, we had 19 students participate.  That is a record by a factor of two.  Our team score was 60 points, another record.  Our top scorer was a high school student in my Calculus II class.  He managed 18.5 points out of 40.  That is another record.

I'm pleased with this year's turn out.  In 2007, my first year, we managed a total of 6.5 team points for both rounds.  That tied for last place in the nation for schools with positive scores.  I would have been less humiliated if we had just scored 0 for the year.

I'm hoping that we will beat one of the other KCTCS schools this year.  Watch out, Madisonville.

Thank you to Susan Strickland for organizing the SML.  I promise to get my results in on time this year.

Update:  It looks like MCTC is the only KCTCS college in the SML competition this year.  We win!!!!!!!

Sunday, November 7, 2010

On Pseudocontext

On the blog dy/dan there has been a discussion about pseudocontext.  Pseudocontext is when a word problem is asking the students to use math that has little to do with the word problem.  Think of the infamous problems with trains leaving stations and moving at different speeds.  I'm having a discussion with another teacher about what qualifies a problem as pseudocontext.  You can check it out here.

I'm trying to finagle a dinner with Gary Rockswold at AMATYC this week in Boston.  I want to get an author's point of view on the subject of pseudocontext.

By the way, I want credit for the word "homocontextmorphism".

Saturday, November 6, 2010

ACT Prep (part 3)

I lead my ACT prep class this morning at Bracken County High School.  It was weird to teach in a high school.  I've taught high school students before, but the classes were at the college.  I was on their home field.  To add to the pressure, there was one of the high school teachers observing me.  The high school is going to be holding ACT Prep classes after school.

It went better today than before.  I think that holding the session in the morning helped.  Usually we have the sessions at night on weekdays and the students are tired after a day of school.  I changed my methods a bit, and actually reviewed the topics like I was teaching them.  The students were more engaged.

I followed the same format as before.  I gave a fifteen minute presentation on the format of the test and a few test taking hints.  Then, I let the students take a practice test for twenty minutes.  Finally, we reviewed the questions for the rest of the two hours.

If you are interested, my prepared notes can be downloaded here.  The handwritten notes during the review are here.

ACT Prep (part 2)

I'm finishing my preparations for an ACT prep class tomorrow at Bracken County High School this morning.  I was searching on-line for hints on leading an ACT prep class, and I came across this article about a report that too much time spent on ACT preparation in class can hurt scores.  I remarked in a previous post that I didn't feel like I was helping the students over the course of two hours.  Perhaps two hours is enough after all.

Wednesday, November 3, 2010

Robin Webb Defeats Jack Ditty

A couple of week ago, I remarked on a conversation I had with Jack Ditty.  Last night, Jack Ditty lost his race for Kentucky's 18th Senate District.  This was the only race last night that I was worried about, as the other races had results that I expected.  Ms. Webb has been on the campus before for several events, and has taken the time to interact with the students.  She seems to genuinely care about our college.  Our representative to the Kentucky House, Mike Denham, ran unopposed.  Mike Denham was one of the first students at the college, and has also been a supporter of the college.

Monday, November 1, 2010

Halloween, My Car, and the Night Sky (part 2)

In response to my last post, Sue VanHattum (the only person who reads this blog :-)) asked why the Pleiades are called the Seven Sisters while there are six stars in the logo for Subaru.  I was going to respond in the comments, but I realized that I had too much to say.

The Pleiades from Greek Mythology where seven daughters of Atlas.  According to the myth, Zeus transformed the Pleiades into stars to protect them from the hunter Orion.  Due to the rotation of the Earth, the constellation Orion appears to follow the Pleiades in the night sky.

The Subaru logo represents the five companies that merged to form Subaru's parent company Fuji Heavy Industries.  Apparently the larger star represents the merged companies.  It looks like there is one star (Celaeno) on the right of the picture that is not part of the Subaru logo.  The Greeks must have seen it differently than the Japanese.

I finally remembered where I heard about the date of Halloween.  I saw it on a Jack Horkhimer: Star Gazer segment last year.  This year's version is below.

I just learned that Jack died this year.

Sue also mentioned that the pagans celebrate the periods halfway between the equinoxes and the solstices.  The astronomy professor at my college told me that Groundhog's Day is at the halfway date between the Winter Solstice and the Vernal Equinox.  I was saving that tidbit for February.

Halloween, My Car, and the Night Sky

Out of all of the superstitions that people have come up with, astrology makes the most sense to me.  I can imagine an ancient person watching the sky and being amazed by how the change of seasons coincide with the change in the stars' position from one night to the next.  It's not far of a leap to think that the position of the stars affected the seasons.

Most people do not plan their lives around the stars anymore, but there are some artifacts of astrology that are still observed.  One of those artifacts is the date of Halloween.  The date of Halloween is October 31st because that used to be the date that the Pleiades would be at their highest at midnight.  This date was set several thousand years ago, and due to the movement of the galaxy, the Pleiades reach their highest point at midnight in mid-November.

The belief was that a bridge between heaven and Earth was formed on Halloween and the dead were able to move back and forth.  Most of our traditions were formed out of this belief.

The Pleiades, or the seven sisters is an open cluster of stars located in the constellation Taurus.  It is one of the Messier objects (M45), and is visible to the naked eye.  A picture I took of the Pleiades is below.  The Earth's rotation and the length of the exposure causes the double images of the stars.
My Photo of the Pleiades
Here is a professional photo from Wikipedia.
A Professional Photo
You may be wondering what is the connection between Halloween and my car.  The Japanese name for the Pleiades is Subaru.  Look at the picture of the logo from my car and compare with the pictures above.